The property suffix tree with dynamic properties

Recently there has been much interest in the Property Indexing Problem ([1],[7],[8]), where one is interested to preprocess a text T of size n over alphabet Σ (which we assume is of constant size), and a set of intervals π over the text positions, such that give a query pattern P of size m we can report all of the occurrences of P in T which are completely contained within some interval from π. This type of matching is extremely helpful in scenarios in molecular biology where it has long been a practice to consider special areas in the genome by their structure. The work done so far has focused on the static version of this problem where the intervals are given a-priori and never changed. This paper is the first to focus on several dynamic settings of π including an incremental version where new intervals are inserted into π, decremental version where intervals are deleted from π, fully dynamic version where intervals may be inserted or deleted to or from π, or batched insertions where a set of intervals is inserted into π. In particular, the batched version provides us with a new (optimal) algorithm for the static case.